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# Estimation: Sample size

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A bank wants to estimate the mean dollars that each card holder will spend each month. It would like to be within plus or minus \$10 of the true mean with a 98% confidence level. The standard deviation is thought to be \$500. How many card holders should be sampled? After you've determined how many card holders should be sampled, the bank comes back and says that it will cost \$5 per sample and they were only planning on spending \$10,000 on the sample. In a memo to the bank product development team indicate how many card holders should be sampled to meet the original requirements of the sample. The explain the trade-offs that will occur when you lower the sample to \$10,000 to meet their budget.

https://brainmass.com/statistics/confidence-interval/estimation-sample-size-32415

#### Solution Preview

Standard deviation =&#963;= \$500
confidence interval= 98%

This is a two tailed test since we are checking for both plus or minus \$10
Let the true mean be \$&#956;
What this problem is saying that we should be in the range \$&#956;+10 and \$&#956;-10 and

With sampling we determine the confidence interval of \$&#956;+Z &#963;x and \$&#956;-Z &#963;x
where
Z is read from the normal probability distribution tables corresponding to ...

#### Solution Summary

Estimation-Sample size: The sample size for estimating the mean amount spent by card holders is calculated.

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